Problem: The function $f(x)$ satisfies
\[f(xy) = xf(y)\]for all real numbers $x$ and $y.$  If $f(1) = 25,$ find $f(79).$
Explanation: Setting $x = 79$ and $y = 1,$ we get
\[f(79) = 79f(1) = 79 \cdot 25 = \boxed{1975}.\]